Method of determining a set of metrology points on a substrate, associated apparatus and computer program

Abstract

A method of determining a set of metrology point locations, the set including a subset of potential metrology point locations on a substrate, the method including: determining a relation between noise distributions associated with a plurality of the potential metrology point locations using existing knowledge; and using the determined relation and a model associated with the substrate to determine the set.

The invention claimed is: 
     
       1. A method of determining a set of metrology point locations, the set comprising a subset of potential metrology point locations on a substrate, the method comprising:
 determining, by a hardware computer system, a relation between noise distributions associated with a plurality of the potential metrology point locations using existing knowledge; and 
 using the determined relation and a model associated with the substrate to determine the set. 
 
     
     
       2. The method according to  claim 1 , wherein the relation describes covariance between each of the plurality of potential metrology point locations. 
     
     
       3. The method according to  claim 2 , wherein the relation has the shape of a covariance matrix and the method further comprises, for each of the potential metrology point locations, minimizing the determinant of a matrix which is formed from: a design matrix describing the model with the respective potential metrology point location; and the covariance matrix. 
     
     
       4. The method according to  claim 1 , wherein the relation includes a relative magnitude of variances associated with the noise distributions. 
     
     
       5. The method according to  claim 1 , wherein the metrology point locations contained in the set are the metrology point locations which contribute the greatest level of informativity about the substrate for a pre-determined size of the set. 
     
     
       6. The method according to  claim 1 , further comprising performing a metrology operation on the substrate using measurements obtained exclusively from metrology points located at the set of metrology point locations. 
     
     
       7. The method according to  claim 1 , further comprising performing an alignment operation on the substrate using measurements obtained exclusively from metrology points located at the set of metrology point locations, during a lithographic process. 
     
     
       8. The method according to  claim 7 , further comprising performing a patterning operation on the substrate after performing the alignment operation. 
     
     
       9. The method according to  claim 1 , further comprising modelling distortions in a lithographic process using measurements obtained exclusively from metrology points located at the set of metrology point locations. 
     
     
       10. The method according to  claim 1 , wherein the existing knowledge includes previous measurements of noise data associated with the metrology point locations. 
     
     
       11. An apparatus having a processor specifically configured to carry out the method according to  claim 1 . 
     
     
       12. A method of determining a model for fitting measurements, the model comprising a plurality of pre-determined base functions and coefficients associated with each of those base functions, the method comprising:
 determining, by a hardware computer system, a relation between noise distributions associated with a plurality of measurement positions using existing knowledge; and 
 using the determined relation and calculated values of each base function at the measurement positions to determine the coefficients. 
 
     
     
       13. The method according to  claim 12 , wherein the relation describes covariance between each of the plurality of measurement positions. 
     
     
       14. The method according to  claim 12 , wherein the relation includes a relative magnitude of variances associated with the noise distributions. 
     
     
       15. The method according to  claim 12 , wherein the determining the coefficients uses a least squares approach. 
     
     
       16. The method according to  claim 12 , wherein the determining the coefficients includes calculating a maximum likelihood estimator of a vector comprising the coefficients. 
     
     
       17. A computer program product comprising a non-transitory computer-readable medium having instructions therein, the instructions, when executed by a computer system, configured to cause the computer system to at least:
 determine a relation between noise distributions associated with a plurality of measurement positions using existing knowledge; and 
 use the determined relation and calculated values of each base function of a plurality of pre-determined base functions of a model for fitting measurements at the measurement positions to determine coefficients associated with each of those base functions. 
 
     
     
       18. An apparatus having a processor specifically configured to carry out the method according to  claim 12 . 
     
     
       19. A computer program product comprising a non-transitory computer-readable medium having instructions therein, the instructions, when executed by a computer system, configured to cause the computer system to at least:
 determine a relation between noise distributions associated with a plurality of potential metrology point locations on a substrate using existing knowledge; and 
 using the determined relation and a model associated with the substrate to determine a set of metrology point locations comprising the potential metrology point locations. 
 
     
     
       20. The computer program product according to  claim 19 , wherein the relation describes covariance between each of the plurality of potential metrology point locations.